In mathematics, especially functional analysis, a normal operator on a complex Hilbert space is a continuous linear operator
that commutes with its hermitian adjoint N*:
Normal operators are important because the spectral theorem holds for them. Today, the class of normal operators is well-understood. Examples of normal operators are
- unitary operators:
- Hermitian operators (i.e., selfadjoint operators): ; (also, anti-selfadjoint operators: )
- positive operators:
- normal matrices can be seen as normal operators if one takes the Hilbert space to be .
Read more about Normal Operator: Properties, Properties in Finite-dimensional Case, Normal Elements, Unbounded Normal Operators, Generalization
Famous quotes containing the word normal:
“Normality highly values its normal man. It educates children to lose themselves and to become absurd, and thus to be normal. Normal men have killed perhaps 100,000,000 of their fellow normal men in the last fifty years.”
—R.D. (Ronald David)